Details

sample662.0ms

Algorithm

intervals

Results

370.0ms	75×	body	640	valid
182.0ms	105×	body	1280	valid
52.0ms	16×	body	2560	valid
11.0ms	15×	body	320	valid
8.0ms	32×	body	80	valid
7.0ms	13×	body	160	valid

simplify27.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.0b

localize58.0ms

Local error

Found 2 expressions with local error:

1.4b	(- (tan (+ x eps)) (tan x))
4.6b	(tan (+ x eps))

rewrite603.0ms

Algorithm

rewrite-expression-head

Rules

4×	`tan-quot` `add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
2×	`pow1` `add-exp-log` `add-cube-cbrt` `tan-sum` `frac-sub` `add-cbrt-cube`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 25

Calls

2 calls:

581.0ms	(- (tan (+ x eps)) (tan x))
16.0ms	(tan (+ x eps))

series734.0ms

Counts

2 → 6

Calls

2 calls:

615.0ms	(- (tan (+ x eps)) (tan x))
112.0ms	(tan (+ x eps))

simplify10.3s

Counts

31 → 31

Iterations

Iter	Nodes
done	5001
4	1771
3	705
2	297
1	135
0	68

prune742.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 13.0b

localize121.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
0.2b	(+ (tan x) (tan eps))
0.3b	(* (tan x) (tan eps))
2.3b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite749.0ms

Algorithm

rewrite-expression-head

Rules

27×	`*-un-lft-identity`
22×	`add-sqr-sqrt`
15×	`add-cube-cbrt`
13×	`times-frac`
9×	`tan-quot`
8×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
6×	`pow1`
5×	`distribute-lft-out`
4×	`associate-/l*`
3×	`associate-r` `associate-l` `associate-/r*` `associate-/l/`
2×	`flip3--` `flip3-+` `frac-add` `associate-/r/` `flip--` `flip-+` `difference-of-squares`
1×	`cbrt-undiv` `+-commutative` `frac-times` `sub-neg` `frac-2neg` `diff-log` `associate-r/` `div-exp` `pow-prod-down` `associate-l/` `prod-exp` `clear-num` `sum-log` `*-commutative` `frac-sub` `cbrt-unprod` `div-inv` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 86

Calls

4 calls:

108.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
145.0ms	(+ (tan x) (tan eps))
34.0ms	(* (tan x) (tan eps))
438.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series4.5s

Counts

4 → 12

Calls

4 calls:

1.2s	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
537.0ms	(+ (tan x) (tan eps))
423.0ms	(* (tan x) (tan eps))
2.3s	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify14.3s

Counts

98 → 98

Iterations

Iter	Nodes
done	5005
3	4395
2	1155
1	411
0	172

prune3.7s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 12.9b

localize162.0ms

Local error

Found 4 expressions with local error:

0.2b	(+ (tan x) (tan eps))
0.2b	(* (sin x) (sin eps))
0.3b	(/ (* (sin x) (sin eps)) (* (cos eps) (cos x)))
2.3b	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (sin eps)) (* (cos eps) (cos x))))) (tan x))

rewrite1.1s

Algorithm

rewrite-expression-head

Rules

18×	`add-exp-log` `add-cbrt-cube`
13×	`add-sqr-sqrt`
10×	`*-un-lft-identity`
8×	`add-log-exp`
6×	`pow1` `add-cube-cbrt`
5×	`prod-exp` `cbrt-unprod`
4×	`cbrt-undiv` `div-exp`
3×	`tan-quot` `associate-r` `associate-l`
2×	`times-frac` `sin-mult` `difference-of-squares`
1×	`+-commutative` `sub-neg` `flip3--` `frac-2neg` `flip3-+` `diff-log` `pow-prod-down` `frac-add` `clear-num` `associate-/r` `sum-log` `associate-/r/` `cos-mult` `-commutative` `frac-sub` `flip--` `flip-+` `div-inv` `associate-/l/` `distribute-lft-out` `associate-/l*` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 71

Calls

4 calls:

18.0ms	(+ (tan x) (tan eps))
50.0ms	(* (sin x) (sin eps))
52.0ms	(/ (* (sin x) (sin eps)) (* (cos eps) (cos x)))
1.0s	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (sin eps)) (* (cos eps) (cos x))))) (tan x))

series2.7s

Counts

4 → 12

Calls

4 calls:

484.0ms	(+ (tan x) (tan eps))
178.0ms	(* (sin x) (sin eps))
374.0ms	(/ (* (sin x) (sin eps)) (* (cos eps) (cos x)))
1.7s	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (sin eps)) (* (cos eps) (cos x))))) (tan x))

simplify4.7s

Counts

83 → 83

Iterations

Iter	Nodes
done	5024
2	1588
1	434
0	173

prune3.7s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 12.8b

localize186.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sin eps) (cos eps))
0.2b	(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
0.3b	(* (tan x) (tan eps))
6.7b	(- (/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite1.0s

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
21×	`add-sqr-sqrt`
14×	`add-cube-cbrt`
12×	`times-frac`
8×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
6×	`pow1`
5×	`tan-quot`
3×	`associate-r` `associate-l` `associate-/r` `associate-/l`
2×	`distribute-lft-out` `difference-of-squares`
1×	`cbrt-undiv` `+-commutative` `frac-times` `sub-neg` `quot-tan` `flip3--` `frac-2neg` `flip3-+` `diff-log` `associate-r/` `div-exp` `pow-prod-down` `associate-l/` `frac-add` `prod-exp` `clear-num` `sum-log` `*-commutative` `frac-sub` `flip--` `cbrt-unprod` `flip-+` `div-inv` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 79

Calls

4 calls:

21.0ms	(/ (sin eps) (cos eps))
72.0ms	(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
36.0ms	(* (tan x) (tan eps))
880.0ms	(- (/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (* (tan x) (tan eps)))) (tan x))

series4.0s

Counts

4 → 12

Calls

4 calls:

107.0ms	(/ (sin eps) (cos eps))
544.0ms	(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
378.0ms	(* (tan x) (tan eps))
3.0s	(- (/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify11.1s

Counts

91 → 91

Iterations

Iter	Nodes
done	5000
3	3855
2	1181
1	414
0	177

prune1.9s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 11.6b

regimes984.0ms

Accuracy

90.8% (0.8b remaining)

Error of 14.2b against oracle of 13.4b and baseline of 22.1b

bsearch3.2s

Steps

Iters	Range		Point
9	1.9019117058808816e-98	1.1854250517603695e-92	1.1710088927834064e-92
10	-9.843551556642301e-53	-9.050756944828755e-64	-9.693921329330396e-53

simplify21.0ms

Iterations

Iter	Nodes
done	52
1	52
0	39

end0.0ms

sample47.4s

Algorithm

intervals

Results

22.0s	3298×	body	1280	valid
8.9s	1846×	body	640	valid
7.0s	646×	body	2560	valid
5.4s	742×	body	320	valid
1.7s	333×	body	160	valid
1.6s	1135×	body	80	valid